I don't know if these companies are still in existence since we take our own car to West Palm for flights, but we did pick up a couple of cards when we first started coming down. Here they are: Palm Beach Transportation, Inc. YELLOW CAB: 1-561-689-2222 and one for their private limo/town cars/vans is 1-561-684-9900. Hope this helps.
Another option is the Tri-Rail (train). You would need a bus or a cab from PBI to the station and maybe from the station to the hotel, but it would be probably cheaper, take about the same time and, more important, no traffic!